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When an input vector is given to an MLP it computes a function. The function F* which the MLP computes has the weights and biases of each nodes as a parameter. Let W be a vector which contains all the weights and biases associated with the MPL as its elements, thus the MLP computes the function F*(W,x).

No specific answer is known till date. The size of the network depends on the complexity of the problem at hand and the training accuracy which is desired. A good training accuracy does not always means a good network. If the number of free parameters of the network is almost the same as the number of data points, the network tends to memorize the data and gives bad generalization.

How many hidden layers to use ?

It has been proved that a single hidden layer is sufficient to do any mapping task. But still experience shows that multiple hidden layers may be sometimes simplify learning.

No, it can generalize only on data points which lies within the boundary of the training sample. The output given by an MLP is never reliable on data points far away from the training sample.

Can I get the explicit functional form of the relationship that exists in my data from the trained MLP?

No, one may write a functional form of nested sigmoids, but it will (in almost all cases) be far from useful. MLPs are black-boxes, one cannot retrieve the rules which governs the input-output mapping from a trained MLP by any easy means.